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A transformation for an $ n$-balanced $ \sb 3\Phi\sb 2$


Author: H. M. Srivastava
Journal: Proc. Amer. Math. Soc. 101 (1987), 108-112
MSC: Primary 33A30; Secondary 05A30
DOI: https://doi.org/10.1090/S0002-9939-1987-0897079-3
MathSciNet review: 897079
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Abstract: An interesting generalization of the familiar $ q$-extension of the Pfaff-Saalschütz theorem is proved and is applied, for example, to derive a reduction formula for a certain double $ q$-series. The main theorem (asserting the symmetry in $ n$ and $ N$ of a function $ f(n,N)$ defined in terms of an $ n$-balanced basic (or $ q{\text{ - }}$-) hypergeometric $ _3{\Phi _2}$ series by equation (8)) is essentially a $ q$-extension of Sheppard's transformation.


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DOI: https://doi.org/10.1090/S0002-9939-1987-0897079-3
Keywords: Pfaff-Saalschütz theorem, basic (or $ q - $-) hypergeometric series, $ n$-balanced series, Sheppard's transformation, Gaussian (or $ q$-binomial) coefficient, Jackson's sum, $ q$-series identity, Sears's transformation, combinatorial analysis
Article copyright: © Copyright 1987 American Mathematical Society

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